For conventional water or liquid storage devices such as water towers for industrial or civil purposes, reservoirs for breeding, or stools, a water-intake control valve is needed to install inside a storage device for automatically supplying water as the water level is low. One kind of conventional water-intake control valves is revealed by Hwang in U.S. Pat. No. 6,823,890 B1. A float body such as a hollow float ball is used to maintain the water level by connecting with a water-intake control valve which opens or closes depending on the water level. When the water level in a storage device is low, the valve/valve stopper of a conventional water-intake control valve will open to supply water flowing into the storage device. On the other hand, when the water level reaches a certain height, the valve/valve stopper will close to stop water flowing into the storage device. Unfortunately, the conventional water-intake control valve cannot adjust the water level by the user's demand since the rotational angle of the float ball is fixed. Therefore, it becomes inconvenient to the users and inefficient in water storage for being unable to change the maximum capacity of a storage device. If a user need to change the water-level upper limit, he has to change the water-intake control valve with a linkage rod of a different length or a different bending angle, which costs money and wastes time.